In efforts to increase performance of secondary batteries, higher energy densities are expected therefrom. A higher energy density can be obtained, for instance, by increasing the operating voltage of a battery (by increasing the battery voltage). For example, Japanese Patent Application Publication No. 2002-042814 (PLT 1) discloses a non-aqueous secondary battery using a positive electrode active material consisting of a spinel lithium nickel manganese composite oxide represented by a prescribed general formula as a non-aqueous secondary battery that exhibits an operating voltage of 4.5 V or above versus lithium metal.